What is the natural orgin and rariety of topaz?????

Answer 1

Topaz is Al2[(F,OH)2|SiO4]

Its origin as a mineral is from fluorine-bearing vapors given off during the last stages of the solidification of igneous rocks. It is found in cavities in rhyolite lavas and granite. It is often found in pegmatites (a very coarse grain igneous rock often of granite).

Rarity is a relative thing. Topaz as a mineral is common. Flawless gem grade topaz however, is more rare, and certain colors when natural are even more rare. Blue topaz is a rare form in nature, but the development of techniques to make plain topaz into blue topaz by treatment with heat and radiation have made blue topaz common and reduced its value considerably.
See:
http://www.palagems.com/blue_topaz.htm

Also see:
http://www.mindat.org/min-3996.html

Other source:
Klein, C. and C.S. Hurlbut, 1977, Manual of Mineralogy, New York: John Wiley and Sons, Inc., page 457-458

Answer 2

Topaz (Al2SiO4(F,OH)2) is a fairly common silicate mineral. It can be found in the Ural and Ilmen mountains, Afghanistan, Czech Republic, Germany, Norway, Pakistan, Italy, Sweden, Japan, Brazil, Mexico, and the United States.

It can come in many colours, but a lot of it used for gems is heat treated to produce more vibrant colours.